Probability Bivariate Density & Distribution Functions

We are starting a chapter on probability distribution functions with two variables. In this lesson, we are going to talk about Bivariate density and Bivariate distribution functions. The idea now is that we have two variables, Y1 and Y2. For example, you might be a student taking a certain number of units at college. Y1 is the number of math units student has taken and Y2 is the number of computer science units that a student has taken. We'll see some interesting properties of the density function, and see how we can calculate probabilities.

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Last reply by: Dr. William MurrayWed Apr 8, 2015 6:06 PM

Post by Arash Mosharrafon April 6, 2015

Thanks for the great lecture. I have the below problem that has to do with the joint density function. I just wanted to make sure I did it right.

A firm manufactures electronic equipment. Total production time per unit is the sum of the time it takes to assemble the item (assembly time), and how long it takes to inspect the item and package it (packing time). Suppose that assembly time is a random variable (X) ranging from 20 minutes to 40 minutes, and packing time is a random variable (Y) ranging from 5 minutes to 15 minutes. Assume that assembly time and packing time are independent and jointly uniformly distributed.a. State the joint probability density function of X and Y, fXY (x, y) .b. The production line must pause whenever a unit takes more than 45 minutes to produce in total. Whatis the probability this will occur? Show how you obtain your answer.

I stated the joint probability function as double integral of fXY(x,y) dydx=1 with bounds [20-40]and [5-15] on the first and second integral respectively.

For the second part I drew a rectangle with the width of 10-40 and 5-15 on the XY axis and then guessed in order to get to 45 min, if the assembly time is 40 the packing time should be 5 and if the packing time is 15(its max) the assembly time must be 35. Then I drew and line and calculated he area of that rectangle and multiplied by 1/200. I was wondering if I did it right and if yes whether there is another way I could do this. Thank you.

Bivariate Density & Distribution Functions

Bivariate Density & Distribution Functions

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.